One-way ANOVA model for categorical data

I have data to fit a one-way ANOVA model to categorical data. I used a simple model first, getting significant coefficients, but with an $R^2$ of 0.2.

I then tried a log model and got more significant coefficients, but the $R^2$ is still only 0.3.

Is this normal for categorical data? Are there any other methods I should try to improve the model?